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We present first results for the $2 \to 4$ single-parton scattering $g g \toc \bar c c \bar c$ subprocess for the first time fully within the$k_t$-factorization approach. In this calculation we have used theKimber-Martin-Ryskin unintegrated gluon distribution which effectively includessome class of higher-order gluon emissions, and an off-shell matrix elementsquared calculated using recently developed techniques. The results arecompared with our earlier result obtained within the collinear-factorizationapproach. Only slightly larger cross sections are obtained than in the case ofthe collinear approach. Inclusion of transverse momenta of gluons entering thehard process leads to a much stronger azimuthal decorrelation between $c c$ and$\bar c \bar c$ than in the collinear-factorization approach. A comparison topredictions of double parton scattering (DPS) results and the LHCb datastrongly suggests that the assumption of two fully independent DPS ($g g \to c\bar c \otimes g g \to c \bar c$) may be too approximate.

Production of two charm quark-antiquark pairs in single-parton scattering within the $k_t$-factorization approach